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Bonding in sulfur-oxygen compounds—HSO/SOH and SOO/OSO: an example of recoupled pair # bonding Beth A Lindquist, Tyler Y Takeshita, David E. Woon, and Thom H. Dunning J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/ct4006536 • Publication Date (Web): 15 Aug 2013 Downloaded from http://pubs.acs.org on August 20, 2013

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Journal of Chemical Theory and Computation

Bonding in sulfur-oxygen compounds—HSO/SOH and SOO/OSO: an example of recoupled pair π bonding Beth A. Lindquist, Tyler Y. Takeshita, David E. Woon and Thom H. Dunning, Jr.* Department of Chemistry, University of Illinois at Urbana-Champaign, 600 S. Mathews Avenue, Urbana, IL, 61801

ABSTRACT. The ground states (X2A″) of HSO and SOH are extremely close in energy, yet their molecular structures differ dramatically, e.g., re(SO) is 1.485 Å in HSO and 1.632 Å in SOH. The SO bond is also much stronger in HSO than in SOH: 100.3 kcal/mol versus 78.8 kcal/mol [RCCSD(T)-F12/AVTZ]. Similar differences are found in the SO2 isomers, SOO and OSO, depending on whether the second oxygen atom binds to oxygen or sulfur. We report generalized valence bond and RCCSD(T)-F12 calculations on HSO/SOH and OSO/SOO and analyze the bonding in all four species. We find that HSO has a shorter and stronger SO bond than SOH due to the presence of a recoupled pair bond in the π(a″) system of HSO. Similarly, the bonding in SOO and OSO differs greatly. SOO is like ozone and has substantial diradical character, while OSO has two recoupled pair π bonds and negligible diradical character. The ability of the sulfur atom to form recoupled pair bonds provides a natural explanation for the dramatic variation in the bonding in these and many other sulfur-oxygen compounds.

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I. Introduction Peculiarities abound in the chemistry of the main group elements in the second (Al-Ar) and subsequent rows of the periodic table. For example, the HSO and SOH isomers differ little in energy (just 4.2 kcal/mol1), yet the SO bond lengths in the two isomers differ by 0.14 Å1, and as we will show, the S-O bond energies differ by more than 21 kcal/mol. In a similar vein, the reactivity of sulfur dioxide (SO2) and ozone (O3) differ dramatically despite the similarities in the description of the electronic structure of these two molecules given in many chemistry texts.2 Clearly, there are gaps in our understanding of the fundamental factors that control molecular structure, energetics and reactivity in the main group elements beyond the first row. In previous papers,3-9 our research group found that a new type of chemical bond—the recoupled pair bond—accounts for many of the differences in the properties of molecules containing the late p-block elements of the first and subsequent rows of the periodic table. A recoupled pair bond differs from a covalent bond in that it involves three electrons. For two atoms to form a recoupled pair bond, the electron in a singly occupied orbital forms a bond with an electron that was a member of a lone pair on the other atom. In the case of the late p-block elements, the p2 lone pair of electrons can be uncoupled from one another to form a bond with an incoming ligand. Recoupled pair bond energies, while smaller than the corresponding covalent bonds, can still be significant, especially when the element containing the lone pair is in the second row or beyond and when the ligand is very electronegative. The ability of elements such as sulfur to form recoupled pair bonds with halides explains: •

Occurrence of hypervalent species of second row elements, such as SF4/SF6, which do not exist for the first row elements.


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•

Presence of excited states in compounds of second row elements that are either only weakly bound or absent in the corresponding first row compounds, e.g., the SF(4Σ–) state.

•

Dramatic variations in sequential bond energies in second row compounds such as in De(Fn-1S–F), n = 1-6.

•

Edge mechanism for molecular inversion in heavily halogenated tri-coordinated species of the second row elements.

•

Reactions involving compounds of the second row elements that have no correspondence in compounds of the first row elements.

For an overview of the above, see Ref. 4. There is great interest in the chemistry of inorganic sulfur-oxygen compounds because of their importance in atmospheric chemistry, organic chemistry, battery electrolytes, and many other applications.10-12 For example, HSO and SOH have garnered much theoretical and experimental consideration because HSO is thought to catalyze ozone depletion.11,13-15 In this and a subsequent paper, we will show that recoupled pair bonding explains the anomalies noted above in HSO versus SOH and OSO versus SOO (this paper) and O3 versus SO2 (the following paper). The recoupled pair bonds in all of our previous studies were in σ systems, but it is also possible to form recoupled pair bonds in π systems. Recoupled pair π bonds affect the structures, the energetics and, ultimately, the reactivity of these molecules. In this paper, we will illustrate the impact of recoupled pair bonds in π systems by comparing a number of properties of HSO versus SOH and OSO (SO2) versus SOO. The former pair of compounds arises from addition of a monovalent species (H) to SO, the latter pair from an addition of a divalent species (O) to SO.


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The remainder of the paper is organized as follows. In Section II, the computational methodology will be discussed. In Section III, the electronic structure of the 3Σ– ground state of SO will be examined. We will illustrate the impact of recoupled pair π bonding by comparing the X2A″ and A2A′ states of HSO and SOH in Section IV. In Section V, we will discuss the analogous comparison of OSO (SO2) and SOO. Section VI will summarize our conclusions. II. Computational methodology Valence bond (VB) theory is a theoretical framework that describes chemical bonding in terms of atomic orbitals. Unlike molecular orbital (MO) theory, VB wavefunctions display the correct behavior upon dissociation and thus are well suited for describing bond making and breaking processes. However, the atomic orbitals are typically not allowed to change as a function of nuclear geometry in a VB calculation. Therefore, in order to describe the often-substantial changes in the atomic orbitals caused by molecular formation, many structures corresponding to both covalent and ionic states must be included in the VB calculation, which can complicate the analysis of bonding in the molecule. Another strategy for overcoming this issue is to optimize the VB orbitals self consistently for each nuclear geometry. The resulting wavefunction is called a generalized valence bond (GVB) wavefunction, although it is referred to as a spin-coupled valence bond (SCVB) wavefunction by others.16,17 The GVB wavefunction contains only one orbital structure, which facilitates the interpretation of the calculation. The GVB wavefunction for an atom or molecule is: n

!GVB = Aˆ! d1! d1!! dn ! dn " a1! a2 !! an "# !!" ! Sa,M d

d

a

(1)

where nd is the number of doubly occupied core and valence orbitals, na is the number of singly n

a occupied active orbitals, and ! S,M is a linear combination of the spin functions for the na active


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electrons with a given total spin (S) and spin projection (M). The spin functions represent the different ways the spins of the electrons in the active orbitals can be coupled. When describing bond formation, both the orbitals and the coefficients of the spin couplings change as the internuclear distance decreases from those appropriate for the atoms (or fragments) to those appropriate for the molecule. GVB theory differs from MO theory in that the active orbitals (φai) are singly occupied and allowed to be nonorthogonal (the active GVB orbitals are orthogonal to the doubly occupied core and valence orbitals, φdi, which are also orthogonal to each other). The computational cost grows rapidly with the number of non-orthogonal singly occupied orbitals and spin functions. Traditionally, the perfect pairing (PP) and strong orthogonality (SO) constraints were invoked to minimize the computational cost.18 In the PP spin function, the pairs of electrons are singlet coupled, each with a spin function of

1 (!" 2

# "! ) :

ϕa1 is paired with ϕa2, ϕa3 is paired with ϕa4,

etc. with any remaining unpaired electrons coupled as appropriate for the given spin state, (S, M). In the PP approximation, only this spin function is included in the calculation. In the SO approximation, the non-singlet paired orbitals in the PP wavefunction are forced to be orthogonal. Improvements in computational power and mathematical algorithms have enabled full GVB calculations to be performed for many chemical species. In this work, we will present the results of both types of GVB calculations: GVB(SO/PP) and full GVB. All calculations were performed with the Molpro suite of quantum chemical programs.19 The GVB calculations were performed using the fully variational CASVB program of Cooper and coworkers20 with Kotani spin functions.21 Only the valence a″(π) orbitals, as well as the SO σ bond in HSO and SOH, were included as active orbitals in the GVB calculations, and orthogonality between the σ and the π orbitals was enforced. Initial guesses for the GVB orbitals


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were derived from a CASSCF wavefunction with the same active space.22,23 The explicitly correlated coupled cluster program in Molpro, RCCSD(T)-F12 with the “a” approximation, was used to perform all coupled cluster calculations in this work.24-27 Explicitly correlated methods can more efficiently represent the exact electronic wavefunction by including terms that depend explicitly on the interelectronic distance. A calculation with an explicitly correlated methodology and a triple zeta basis set typically has an accuracy comparable to that from a quadruple or quintuple zeta basis set without the explicitly correlated terms.28 Triple-zeta correlation consistent basis sets were used for all calculations reported herein [aug-cc-pVTZ29,30 on hydrogen and oxygen and aug-cc-pV(T+d)Z31 on sulfur]. We use GVB orbital diagrams to schematically represent the electronic configurations and wavefunctions of the molecules of interest. In these diagrams, the three p orbitals of sulfur and oxygen are depicted as follows: the two p orbitals in the plane of the paper are drawn as two lobes; the p orbital that points out of and behind the plane of the paper is drawn as a small circle. The dots represent the electron occupations of the p orbitals. The hydrogen atom is depicted as a *,#

./#

!"#$#%&'(#

circle with a dot (electron) at the center, representing the 1s orbital; see Figure 1. We

*+#

)#%&'(#

*-#

will introduce additional notation in the

Figure 1. GVB orbital diagrams for the sulfur,

following

section

appropriate

for

oxygen and hydrogen atoms.

representing bonding of recoupled sulfur π orbitals.


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III. The ground X3Σ - state of SO A. The MO description of bonding in SO The ground state of SO has 3Σ– symmetry.

(a)

The singlet states, 1Δ and 1Σ+, arising from !"

#"

!"

#"

(b)

the π2 configuration lie at higher energies, in accordance with Hund’s Rule.32 The

Occ=2.0

Occ=2.0

Occ=1.0

calculated equilibrium bond energy and bond length of SO(X3Σ–) are De = 125.2 kcal/mol and re = 1.483 Å [RCCSD(T)-

Figure 2. (a) Orbital diagrams for the Hartree

F12/AV(T+d)Z], which compare well with

Fock (HF) configuration of SO(X3Σ–) and (b)

the experimental values of De = 125.2

select localized HF orbitals. Throughout the

kcal/mol and re = 1.4933 Å.33 This bond

paper, the location of the oxygen atoms is

length is substantially shorter than would be

depicted by a red sphere and that of the sulfur

anticipated for a single bond based on the

atom by a yellow sphere.

sum of the covalent radii of the S and the O atoms (1.71 Å),34 suggesting a contribution

from the π electrons to bonding in SO. The orbital diagrams, including the π electrons, for the Hartree Fock (HF) configuration of SO(X3Σ–) are given in Figure 2(a), where the singly occupied orbitals are triplet coupled. Both of these resonance structures contribute equally to form a Σ state. The localized HF orbitals are shown in Figure 2(b). As expected, the πx and πy orbitals are equivalent due to symmetry; only the πx orbitals are shown. (The orbitals were localized to remove mixing of the σ bond with the valence s2 pairs of oxygen and sulfur.) In MO theory,


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bonding in the X3Σ– state of SO is described by three doubly occupied bonding orbitals (one σ and two π) and two singly occupied anti-bonding orbitals (both π). Therefore, each π system has a bond order of ½. However, this does not mean that the two π systems within each resonance structure (S3p2 aligned with O2p1 and S3p1 aligned with O2p2) contribute equally to the bonding. In fact, the discrepancies between the molecular structure and energetics of HSO and SOH described in the introduction are suggestive that these two π systems are in fact not equivalent, with the bonding present in HSO (S3p2 aligned with O2p1) making the largest contribution. In Section IV, we will show that recoupled pair π bonding explains why this is the case. However, in order to properly describe recoupled pair bonding, we need to use the GVB wavefunction. B. The GVB description of the sulfur and oxygen atoms To lay the groundwork for describing the GVB diagrams for SO, we will first discuss the GVB orbitals for the sulfur and oxygen atoms. The ground state HF configuration of the sulfur atom is 3s23px3py23pz. The corresponding GVB wavefunction has the configuration 3s23px3py–3py+3pz., i.e., the 3py2 lone pair orbital is described by a pair of singlet-coupled 3p lobe orbitals, (3py–, 3py+). As we will show, these lobe orbitals play a significant role in the formation of recoupled pair π bonds. The sulfur lobe orbitals are a mixture of 3p and 3d orbitals, c13p ± c23d; however, this 3d orbital is not identical to the sulfur atomic 3d orbital and its contribution to the wavefunction (c2) is small. Plots of the sulfur 3pπ lobe orbitals relevant to this study, where the d orbital is the 3dyz orbital, are shown in Figure 3(a). Although the (3py–, 3py+) lobe orbitals are polarized away from one another (a result of the angular correlation provided by the inclusion of 3d orbital in the wavefunction), the overlap of the orbitals is still very high (0.89), a fact that limits the type of recoupled pair bonds that can be formed; see Ref. 4.


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(a)

(b)

In contrast to the sulfur atom, the GVB (2py–, 2py+) orbitals for the oxygen atom involve excitation into the 3py orbital rather (c)

than a 3d orbital. One of these GVB orbitals is concentrated near the nucleus, !"

#"

!"

#"

Figure 3. (a) GVB 3pπ lobe orbitals, (3py–, 3py+), for the ground state of the sulfur atom (3P). (b) GVB 2pπ lobe orbitals, (2py–, 2py+), for the ground state of the oxygen atom (3P). Throughout this work, a dashed line between a pair of GVB orbitals like that separating the sulfur lobes and the oxygen lobes denotes that these orbitals are singlet coupled. (c) Proposed GVB diagrams for

while the other orbital is more diffuse (radial correlation); see Figure 3(b). Prior studies of recoupled pair bonding have demonstrated that it is much more difficult to form a recoupled pair bond with oxygen—a consequence of both the in-out nature of the (2py–, 2py+) GVB orbitals and the more tightly bound nature of the electrons in these orbitals.8

the two resonance structures of SO(X3Σ–).

C. The GVB description of bonding in SO(X3Σ –) In previous works on recoupled pair bonding, two trends were observed: (1) only very electronegative ligands can recouple a p2 electron pair, and (2) the 3p2 pair of sulfur is much easier to recouple than the 2p2 pair of oxygen.8 Therefore, we would predict that the π system that aligns the 3pπ2 orbital on sulfur and the 2pπ1 orbital of oxygen might form a recoupled pair bond. The converse π system containing a 3pπ1 sulfur orbital and a 2pπ2 oxygen orbital is not


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likely to do so. With these guidelines in mind, we propose GVB orbital diagrams for SO(X3Σ–) in Figure 3(c), where the electrons of the sulfur 3p2 pair are represented by two lobes like those plotted in Figure 3(a), each containing one electron. The recoupled pair bond between the singly occupied 2p oxygen orbital and one of the lobes on the sulfur atom is indicated with a pink dashed line. Because we do not expect the 2p2 GVB orbitals of oxygen to be recoupled, we depict it as a doubly occupied orbital in the diagrams, though we do allow the 2p electrons to occupy two lobe orbitals in the GVB calculations. The above description is consistent with the HF orbitals shown in Figure 2(b), where the doubly occupied π orbitals are concentrated on the oxygen atom, with some polarization or delocalization toward the sulfur atom. The singly occupied π orbitals are concentrated on the sulfur atom but have a high degree of anti-bonding character. This indicates that the electrons in these orbitals interact strongly with the electrons in the doubly occupied π orbital with which they are aligned, which would be expected if a recoupled pair bond were present in the π system. However, because the π orbitals are identical due to symmetry, it is not possible to directly observe the differences between the two π systems—one with a recoupled pair π bond and the other without such a bond. In order to circumvent this difficulty, we can add a hydrogen atom to SO to form HSO or SOH. This will lift the symmetry constraints and enable us to observe any recoupled pair π bonding between S and O.


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IV. Results for the HSO and SOH isomers The ground states of HSO and SOH are both X2A″ states; GVB orbital diagrams of their formation from H and SO are shown in Figure 4. At the RCCSD(T)-F12/AV(T+d)Z level of theory without zero-point corrections, the two species are a mere 1.9 kcal/mol separated in energy, with HSO being the more stable species. This near energetic degeneracy is surprising, given the disparate inherent strengths of an OH bond and an SH bond. For instance, the 2Π ground states of OH and SH have dissociation energies of 107.1 kcal/mol and 87.5 kcal/mol, respectively. Therefore, if the SO bond is '$

($

'$

($

unaffected by hydrogen addition, we would expect SOH to be approximately 20

!"

kcal/mol more stable than HSO. However, as the GVB diagrams for the two additions

!"#$%$&$'($ $%'($

!)#$%$&$'($ $'(%$

show, adding a hydrogen atom to the sulfur

Figure 4. GVB orbital diagrams depicting the

or oxygen atoms of SO is fundamentally

formation of ground state HSO (a) and SOH (b)

different if there is a recoupled pair π

from H + SO. In HSO(X2A″), the recoupled pair

bonding

π bond is not broken, but it is in SOH(X2A″).

formation with the oxygen atom would

in

the

SO

molecule.

Bond

disrupt any S-O recoupled pair π bond, weakening that bond. By contrast, bond formation with the sulfur atom will not have a direct effect on the recoupled pair π bond, and so we would expect the S-O bond to be relatively unaffected.


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A. Structures and energetics of HSO and SOH The X2A″ state of HSO has an S-O bond 5678( 9:%

!"#1(%&%

length (re) of 1.485 Å and an S-O bond !"#$"%&'(()*)+,&

!)2")%*+,-./0-%

;5678)< :%

-./01,&'(()*)+,&

energy (De) of 100.3 kcal/mol; see Figure 5.

56;78)< :%

!"#12%&%

!"3()%&%

41"1%*+,-./0-%

!''"(%*+,-./0-% ;56799.9%) singlet couples the two GVB orbitals on the central oxygen atom with a overlap of 0.80, leaving the GVB orbitals on

(b)

φ1

φ2

the terminal atoms singlet coupled with a small, but non-negligible overlap of 0.15. It

φ3

is the latter, weak coupling that gives rise to

φ4

the diradical character of SOO. The bonding in SOO is essentially the same as in the X2A″ state of SOH. The GVB overlaps of Figure 9. Full GVB valence π orbitals of (a)

these states are compared in Table 1, where

SOO (1A′) and (b) OSO at re.

the overlaps from SOO that are analogous to those of SOH (those not involving the π

orbital on the terminal oxygen atom) are boxed in green. The GVB descriptions of the two molecules are quite similar but not identical; the SOO overlaps are slightly reduced in magnitude relative to SOH. This is a result of the more diffuse nature of the π system since it is now spread over an additional atom. The π orbitals of SOO are also polarized towards the more electronegative terminal oxygen atom. Therefore, the unfavorable overlaps of the oxygencentered GVB orbitals are larger (0.43 and 0.21) than those of the sulfur atom and the central oxygen atom (0.42 and 0.11).


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(a)

ϕ1

ϕ1

ϕ2

ϕ3

1.00

0.83

0.16

The bonding in OSO is qualitatively different than in SOO; the dominant spin-coupling coefficient (98.9%) contains two π bonds with

ϕ2

1.00

0.47

ϕ3

1.00

favorable overlaps of 0.71. The overlap between the two GVB orbitals [shown in Figure 9(b)] on the central atom is now

(b)

unfavorable, but reduced to 0.46 (relative to ϕ1

ϕ2

ϕ3

ϕ4

0.89 in the sulfur atom). The overlap between the two terminal GVB orbitals is also

ϕ1 ϕ2

1.00

0.80

0.11

0.21 unfavorable but is just 0.06. The shortening and

1.00

0.42

0.43

1.00

0.15

strengthening of the OSO bonds relative to SO is a direct result of the formation of the

ϕ3

recoupled pair bond dyad and the reduction in

ϕ4

1.00

the unfavorable orbital overlaps. The relevant overlap comparison is shown in Table 2(a) and

Table 1. (a) Overlaps of GVB orbitals for SOH. (b) Overlaps of GVB orbitals for SOO. Favorable overlaps in the dominant spincoupling pattern are given in blue, and unfavorable overlaps are in red.

in the boxed values in Table 2(b). In the X2A″ state of HSO, where the unpaired electron is not forming any bonds, the unfavorable overlaps are 0.62 and 0.18. In OSO however, the electron leftover from formation of the

recoupled pair π bond is bonded to a singly occupied π orbital of the second oxygen atom, which results in its delocalization onto that oxygen atom. This reduces the unfavorable overlaps to 0.46


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(a)

Page 22 of 38

and 0.09. Formation of this bond reduces the ϕ1

ϕ2

ϕ3

favorable overlap from 0.78 to 0.71, but the formation of an additional bond and the

ϕ1

1.00

ϕ2

0.78

0.18

1.00

0.62

ϕ3

reduction of the unfavorable overlaps more than compensates for this decrease.

1.00 It is worth noting that these results are in

(b)

basic agreement with prior GVB studies of ϕ1

ϕ2

ϕ3

ϕ4

sulfur

dioxide.

Unpublished

GVB(SO/PP)

calculations by one of the authors (THDJr) in ϕ1 ϕ2

1.00

0.71

0.09

0.06

1.00

0.46

0.09

1.00

0.71

the early 1980s also showed the formation of two π bonds. Improving on these results by removing the perfect pairing and, more

ϕ3

importantly, removing the strong orthogonality

ϕ4

1.00

constraints, we find orbitals that also describe a π bonded structure, essentially providing OSO

Table 2. (a) Overlaps of GVB orbitals for with two S-O double bonds. Cooper et al.36 also HSO. (b) Overlaps of GVB orbitals for SO2. performed full GVB (SCVB) calculations on Favorable overlaps in the dominant spinthe π system of OSO, although including coupling pattern are given in blue, and different orbitals in the active space. Our unfavorable overlaps are in red. results are in good agreement with theirs. The current work adds to this collection of studies by interpreting the orbitals and rationalizing the differences in bonding with GVB theory and the recoupled pair bonding model. The differences


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in the structure and energetics of the SOO and OSO provide compelling additional evidence for the presence of a recoupled pair π bond in SO(X3Σ–) and dramatically illustrates the effects of recoupled pair bonds and dyads. VI. Conclusion The GVB wavefunction provides unrivaled insights into the nature of bonding in molecules and a clear description of a new type of bond that can be formed by the elements in the second and subsequent rows of the periodic table—the recoupled pair bond. GVB calculations help elucidate the role of recoupled pair bonds and recoupled pair bond dyads in determining the structure, energetics and reactivities of molecules containing these elements. In this paper we used detailed GVB calculations to obtain insights into the remarkable differences between the HSO and SOH isomers, and extended these results to account for the differences between SOO and OSO. A recoupled pair π bond exists in the ground state of SO(X3Σ–), but its presence is masked by symmetry considerations. The presence of the recoupled pair π bond in SO was revealed by lowering the symmetry, namely, adding a hydrogen atom to SO to form HSO and SOH. The recoupled pair π bond persists in HSO but must be broken to form SOH, which accounts for the surprising lengthening and weakening of the SO bond in the ground state of SOH relative to that of HSO. The GVB orbitals of the π system of these molecules possess qualitative differences in their orbital coupling patterns that reflect the presence (HSO) or absence (SOH) of a recoupled pair bond. The results presented here are consistent with prior MO-based calculations on HSO and SOH, although our use of the GVB wavefunction allows us to gain more detailed insights into the description of bonding in these species. For example, a prior NBO analysis of the HSO and SOH wavefunctions showed a greater degree of π bonding in the former, and recoupled pair


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bonding explains why this is so.39 Further, these authors note the small dissociation energy (88.1 kcal/mol) computed for the OH bond in SOH by subtracting the energy of SOH(X2A″) from that of H(1S)+SO(X3Σ–). While this result alone could be due to any number of factors (poor overlap of the O and H atoms or steric repulsion with the incoming hydrogen atom, for instance), our analysis presents a clear explanation for this finding: the presence of the recoupled pair π bond in SO but not in SOH. The small energy difference between HSO and SOH can be understood as a near cancellation of two effects: (1) the inherently greater strength of an OH bond versus an SH bond, which favors SOH over HSO, and (2) the energetics gains from the presence of the recoupled pair bond in HSO but not in SOH, which favors HSO over SOH. The same “veiled” recoupled pair π bond in SO(X3Σ–) also explains the differences in the lengths and strengths of the bonds in SOO and OSO (SO2). The orbital left over from formation of the recoupled pair π bond in SO is concentrated on the sulfur atom. Therefore, an incoming divalent ligand, such as an oxygen atom, approaching the sulfur atom can form both a σ and a π bond to form SO2. The new π bond strengthens the SO bonds, explaining why the bonds in SO2 are shorter and stronger than the bond in the SO diatomic molecule. However, in the converse situation where a divalent ligand bonds with the oxygen atom of SO, the recoupled pair π bond is broken, and there is no longer the possibility of forming a second π bond. The net result is a substantially longer and weaker SO bond in SOO than in either SO2 or SO. As a result, SOO has substantial diradical character and is much less stable than the OSO isomer. The results presented here further demonstrate the utility of the GVB wavefunction and recoupled pair bonding model in explaining the rather dramatic differences in structure and energetics of two isoelectronic sulfur-oxygen compounds. Recoupled pair bonding not only successfully rationalizes these differences, but the results of the calculations are in agreement


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with the predictions made from GVB diagrams. We expect that the findings presented here apply generally to sulfur-oxygen compounds where a doubly occupied sulfur orbital can be aligned with a singly occupied oxygen orbital, and ongoing calculations in our group support the notion that recoupled pair bonding of π electrons should be considered when short SO bond are observed. ASSOCIATED CONTENT Supporting Information Optimized geometries and absolute energies for all species (X2A″ and A2A′ states of HSO and SOH, X1A′ state of SOO and X1A1 state of OSO) presented in this work. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Email: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the Distinguished Chair for Research Excellence in Chemistry and the National Center for Supercomputing Applications at the University of Illinois at UrbanaChampaign. One of the authors (B.A.L.) is the grateful recipient of a National Science Foundation Graduate Research Fellowship.


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REFERENCES (1) Wilson, A. K.; Dunning, T. H. J. Phys. Chem. A 2004, 108, 3129-3133. (2) Purser, G. H. J. Chem. Educ. 1999, 76, 1013-1018. (3) Chen, L.; Woon, D. E.; Dunning, T. H. J. Phys. Chem. A 2009, 113, 12645-12654. (4) Dunning, T. H., Jr.; Woon, D. E.; Leiding, J.; Chen, L. Acc. Chem. Res. 2013, 46, 359368. (5) Leiding, J.; Woon, D. E.; Dunning, T. H. J. Phys. Chem. A 2011, 115, 4757-4764. (6) Leiding, J.; Woon, D. E.; Dunning, T. H. J. Phys. Chem. A 2011, 115, 329-341. (7) Woon, D. E.; Dunning, T. H. J. Phys. Chem. A 2009, 113, 7915-7926. (8) Woon, D. E.; Dunning, T. H. Mol. Phys. 2009, 107, 991-998. (9) Woon, D. E.; Dunning, T. H. J. Phys. Chem. A 2010, 114, 8845-8851. (10) Barnes, I.; Hjorth, J.; Mihalopoulos, N. Chem. Rev. (Washington, DC, U. S.) 2006, 106, 940-975. (11) Tyndall, G. S.; Ravishankara, A. R. Int. J. Chem. Kinet. 1991, 23, 483-527. (12) Zhang, S. S.; Foster, D.; Read, J. J. Power Sources 2010, 195, 3684-3688. (13) Lee, Y. Y.; Lee, Y. P.; Wang, N. S. J. Chem. Phys. 1994, 100, 387-392. (14) Lovejoy, E. R.; Wang, N. S.; Howard, C. J. J. Phys. Chem. 1987, 91, 5749-5755. (15) Wang, N. S.; Howard, C. J. J. Phys. Chem. 1990, 94, 8787-8794. (16) Goddard, W. A.; Dunning, T. H.; Hunt, W. J.; Hay, P. J. Acc. Chem. Res. 1973, 6, 368376. (17) Hiberty, P. C.; Shaik, S. J. Comput. Chem. 2007, 28, 137-151. (18) Bobrowicz, F. W. Goddard, W. A. In Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum: New York, 1977; Vol. 3, pp. 79. (19) MOLPRO, version 2010.1, a package of ab initio programs, Werner, H. J. Knowles, P. J.; Knizia, G.; Manby, F. R.; Schutz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; Shamasundar, K. R.; Adler, T.B.; Amos, R.D.; Bernhardsson, A.; Berning A.; Cooper, D. L.; Deegan, M.J.O.; Dobbyn, A.J.; Eckert, F.; Goll, E.; Hampel, C.; Hesselmann, A.; Hetzer, G.; Hrenar, T.; Jansen, G.; Koppl, C.; Liu, Y.; Lloyd, A.W.; Mata, R.A.; May, A.J.; McNicholas, S.J.; Meyer, W.; Mura, M.E.; Nicklass, A.; O'Neill, D.P.; Palmieri, P.; Pfluger, K.; Pitzer, R.; Reiher, M.; Shiozaki, T.; Stoll, H.; Stone, A.J.; Tarroni, R.; Thorsteinsson, T.; Wang, M; Wolf, A., see http://molpro.net. (20) Thorsteinsson, T.; Cooper, D. L.; Gerratt, J.; Karadakov, P. B.; Raimondi, M. Theor. Chim. Acta 1996, 93, 343-366. (21) Cooper, D. L.; Thorsteinsson, T.; Gerratt, J. Int. J. Quantum Chem. 1997, 65, 439-451. (22) Knowles, P. J.; Werner, H. J. Chem. Phys. Lett. 1985, 115, 259-267. (23) Werner, H. J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053-5063. (24) Knizia, G.; Adler, T. B.; Werner, H. J. J. Chem. Phys. 2009, 130, 054104. (25) Knizia, G.; Werner, H. J. J. Chem. Phys. 2008, 128, 154103. (26) Knowles, P. J.; Hampel, C.; Werner, H. J. J. Chem. Phys. 1993, 99, 5219-5227. (27) Manby, F. R. J. Chem. Phys. 2003, 119, 4607-4613. (28) Adler, T. B.; Knizia, G.; Werner, H. J. J. Chem. Phys. 2007, 127, 221106. (29) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007-1023. (30) Woon, D. E.; Dunning, T. H. J. Chem. Phys. 1993, 98, 1358-1371. (31) Dunning, T. H.; Peterson, K. A.; Wilson, A. K. J. Chem. Phys. 2001, 114, 9244-9253. (32) Hund, F. Zeitschrift Fur Physik 1928, 51, 759-795.


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(33) Huber, K. P. Herzberg, G. Molecular Spectra and Molecules. IV. Constants of Diatomic Molecules; Van Nostrand: Princeton, NJ, 1979. (34) Cordero, B.; Gomez, V.; Platero-Prats, A. E.; Reves, M.; Echeverria, J.; Cremades, E.; Barragan, F.; Alvarez, S. Dalton Trans. 2008, 2832-2838. (35) Pauli, W. Zeitschrift Fur Physik 1925, 31, 765-783. (36) Cunningham, T. P.; Cooper, D. L.; Gerratt, J.; Karadakov, P. B.; Raimondi, M. J. Chem. Soc., Faraday Trans. 1997, 93, 2247-2254. (37) Glezakou, V. A.; Elbert, S. T.; Xantheas, S. S.; Ruedenberg, K. J. Phys. Chem. A 2010, 114, 8923-8931. (38) Chase, M. W.; Davies, C. A.; Downey, J. R.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J. Phys. Chem. Ref. Data 1985, 14, 1-926. (39) Perez-Juste, I.; Carballeira, L. J. Mol. Struc.-Theochem 2008, 855, 27-33.


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For Table of Contents Use Only “Bonding in sulfur-oxygen compounds—HSO/SOH and SOO/OSO: an example of recoupled pair π bonding” Beth A. Lindquist, Tyler Y. Takeshita, David E. Woon and Thom H. Dunning, Jr. singlet-coupled

RECOUPLING!

reduce r(SO)

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Sulfur Addition 1

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125.2 kcal/mol

HSO(X2A )

Oxygen Addition

SOH(X2A )

1.485 Å

1.632 Å

78.8 kcal/mol

100.3 kcal/mol HSO(A2A )

SOH(A2A )

1.654 Å

1.659 Å

66.6 kcal/mol

58.6 kcal/mol 1.494 Å

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SO(a1 )

(a)Journal GVB(SO/PP) orbitals, r=re+1.0 ÅPage 34 of 38 of Chemical Theory and Computation 1 2 3 4 5 6 GVB(SO/PP) orbitals, r=re (b) 7 8 9 10 11 12 13 14 (c) Full GVB orbitals, r=re 15 16 φ φ2 1 17 18 19 ACS Paragon Plus Environment 20 21 22

φ3

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OSO

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